Basic graph theory definitions

Node

A node in a network represents an entity or biological object, such as a protein, gene, metabolite, or any other biological molecule. In biological networks, nodes are the building blocks that represent the individual components of a system, like specific genes in a gene regulatory network or metabolites in a metabolic network.

Edge

An edge represents a connection or interaction between two nodes. In biological networks, edges can represent various types of interactions, such as physical binding between proteins, metabolic conversions, or regulatory relationships between genes. For example, an edge between two proteins could represent a protein-protein interaction (PPI), while an edge between a gene and a protein could signify gene expression regulation. The edges can be undirected or directed as described below:

Undirected edges

Undirected edges are typically represented by a line. The relationship between the nodes is some form of connection, without implying any sort of causality or order in time (Fig 3).

Directed edges 

Directed edges are typically represented by an arrow. The relationship between nodes is hierarchical, it implies causality or an order of events. Directed edges can also indicate whether the relationship between two components is negative (e.g. downregulation or inhibition), typically represented with an arrow with a flat tip, or positive (e.g. upregulation or activation), typically represented by a standard arrow (Fig 3).